DISAGGREGATE MULTIMODAL MODEL FOR WORK TRIPS IN THE NETHERLANDS Moshe Ben-Akiva,

Massachusetts Institute of Technology and Cambridge Systematics, Inc.; and Martin G. Richards, Buro Goudappel en Coffeng, b.v., Netherlands

This paper describes a disaggregate modal-choice model with 6 travel modes (walking, bicycle, moped, car, bus, and train) for work trips. The data used in the study were from 2 communities adjacent to Eindhoven, Netherlands. A number of alternative model specifications were tested, and the results of these tests were analyzed. The model specification that was considered to be the most satisfactory overall is based on treating in­vehicle travel time as a generic variable and out-of-vehicle travel time as a series of modal-specific variables. Out-of-pocket travel costs were found to have no significant influence on modal choice. Although a number of socioeconomic variables were tried, the only ones included in the most satisfactory model were 3 vehicle -availability variables (car, moped, and bicycle) . Analyses of the coefficients estimated in a number of different subsamples of the main sample showed that the marginal decreases in the standard errors of the coefficients were very small for samples containing more than 250 observations. A simple test of the most satisfactory model estimated as an aggregate predictive model indicated that effects of the theoretical problems of using a disaggregate model with aggregate data can be minimized by use of suitable market stratification.

• THIS PAPER presents some of the results of a study to develop disaggregate, be­havioral travel demand models in the Netherlands. The general disaggregate modeling methodology and the multinomial logit model used in this study are described in detail elsewhere (1, 3, 4) and will not be repeated here. The purpose of this paper is to de­scribe the mode.IS that were developed for work trips.

The models predict the short-term modal-choice behavior of a worker; residential location, work place, and automobile ownership are considered as predetermined. The models, therefore, predict the choice of travel mode fol' a given work trip . Other choices that received some attention in this study were between (a) a single trip to work and a double work chain that is taken by wo1·kers who go home for lunch and (b) the choice of both destination and mode for shopping trips (3, 4, 13).

The urban transportation scene in the Netherlands is- characterized by the number of modes available and in common use; bus, car, bicycle, moped, and walking all play a significant part. In the larger urban areas, the train also is used for intraurban trips. In Amsterdam, The Hague, Rotterdam, and Delft, there is an extensive streetcar net­work; the streetcar network in Rotterdam is supplemented by a metro. In 1966, 9.4 percent of all weekday trips in the west of the country were made by public transport. Buses and streetcars accounted for 7.6 percent, and trains accounted for 1.8 peTcent (7). Although 10. 7 percent of all trips made within the 4 major urban areas were by bu s or streetcar, only 1.6 percent of all weekday trips made in the other urban areas were by public transport. In these other urban areas, bicycle and moped predominated and accounted for 55.6 percent of all weekday trips. Even within the 4 major urban areas, bicycle and moped were used for 35. 7 percent of all trips.

The bicycle is a well-established and well-known Dutch phenomenon. The moped is more recent, and the number in use has doubled between 1960 and 1971. The moped is a motorized bicycle with an engine of not more than 50-cm3 capacity; it ca11 be r idden

107

108

by anyone 16 year s old or older . Officially, mopeds are limited to 30 km/ h within built -up areas and 40 km/h elsewhere . In practice, these speed limits are not enforced. Under congested urban conditions, because mopeds have a high degree of maneuver­ability, journey times of mopeds are considerably shorter than those of bus and equal to those of car. Passengers are allowed to be carried, and the Dutch Central Bureau of Statistics estimated that, in 1971, mopeds were used for 9. 77 million passenger-km; private cars were used for 78.4 million passenger-km (5). Thus a conventional binary modal-split model for car and public transport clearly has only limited usefulness, and the bicycle, moped, and walking modes also must be modeled explicitly.

THEORETICAL MODEL

The choice-of-mode-to-work model explains the conditional probabilities of choosing a mode of travel for the work trip given residential and employment locations and given that a trip is made. Thus the dependent variable can be denoted as follows:

P(m:Mt) (1)

or

Pt (m) (2)

where

m = an alternative mode, and Mt = set of available modes for traveler t.

The logit model predicting this probability is written as

eVn11

P(m :Mt) = :E ev .. ·, (3)

m'€M1

where v.1 is the utility of mode m to traveler t for the work trip and can be expressed in the general form

V.1 = V. (z., St) (4)

where

z. =a vector of characteristics of mode m, and S1 = a vector of socioeconomic characteristics of traveler t.

v. 1 is assumed to be a linear function in the parameters.

where

V.t=X:,t9

K = I: x.tk ek

k=l

109

(5)

x.t = a K x 1 vector of finite functions constructed from the varioos z. and St vari­ables and different from one alternative to another = (X,,u, x.t2, ... , XmtK), and

e =a K x 1 vector of coefficients to be estimated for each model= (01, 92, ... , eK).

If a variable appears only in the utility function of mode m, then it is a mode-m­specific variable that takes a value of 0 in all other modal utilities. If a variable ap­pears in the utility function of all modes, then it is a generic variable. The value of a generic variable must not be equal for each alternative (that is, each mode) for all ob­servations, or, mathematically, this variable is canceled out.

DATA

The data for the estimation of the models were taken from a 1970 home-interview travel survey conducted in Eindhoven, the fifth largest city in the Netherlands (1970 population: 190,000), and 4 adjacent municipalities : Best, Veldhoven, Geldrop, and Son and Breugel (2, 12). One particularly relevant cbaracteristic of these data was that the origin­c1estri1ation (O-D) data had been coded to a 10-m rectangular coordinate system. This made identifying the precise locations of the 0-D addresses possible. For this study only, the data for residents of Best and Son and Bruegel were used. Son and Breugel (1970 popult'l.tion: 10,800) is a medium- and high-income area with bus but no train ser­vice to Eindhoven; Best (1970 population: 16,500) is a low-income area with both rail and bus links to Eindhoven.

The trip and socioeconomic data available from the survey were supplemented by transportation level-of-service data collected for this study. Level-of-service data were derived by manually locating each pair of home and work addresses on large-scale plans and by using a variety of information sources including original measurements.

The sample used for estimation was limited to home-work-home chains as opposed to simple home-work trips. This was done to minimize the influence of other choice considerations such as use of car for business purposes during the day. The sample included 390 observations of a single home-work-home chain during the day.

For model evaluation and practical considerations, the sample was divided into 2 different sets of subsamples. One was a random division into 2 equal groups based on whether the reference number of the household was an odd or an even number; these 2 groups were coded SBBl and SBB2. The other was a geographic division into Son and Breugel (SB) and Best (B). The total set of data was coded SBB. This division was intended to allow evaluation of model stability, by comparing the 2 random subsamples, and geographic stability.

The household and personal socioeconomic data were examined to determine whether, on the basis of household vehicle ownership and possession of a driver's license, car, moped, or bicycle could be r egarded as alternative modes. If no vehicles were owned in any of the 3 classes (car, moped, bicycle) then that mode was assumed not to be a valid alternative. Similarly, if the individual was not in possession of a valid driver's license for cars, even if a car was available within the household, then car was not considered to be a valid alternative. (Only car driver was considered as an alternative; car passengers were excluded.) If a destination was more than 2 km away, walk was not considered a relevant alternative mode. Train was considered relevant only from Best to Eindhoven. Bus was not considered a relevant alternative for work trips within Son and Breugel because no such trips by bus were observed.

110

Table 1 gives the distribution of the chosen mode for work trips in the SBB sample. This is compared with the moda l split of weekday trips fo r all purposes in t he west of the Netbel'lands ( 7) .

VARIABLES USED IN THE MODELS

The explanatory variables used in the work modal-choice models are of 2 types: level­of-service and socioeconomic variables . We have denoted the variables by abbrevia­tions. Table 2 gives a list of the variable codes and their descriptions. The following are the code prefixes and what they represent:

Prefix Meaning

B Bus BF Moped c Car F Bicycle

Level-of-Service Variables

Prefix

PT T TW w

Meaning

Public transit Train Two-wheel vehicle Walking

Three level-of-service variables were used in the models.

1. IVTT represents in-vehicle travel time (in minutes). For walking trips, IVTT is always O; for all mechanical modes it is the time spent in or on the vehicle.

2. OVTT represents out-of-vehicle travel time (in minutes). For walking trips, OVTT is the total walking time of the trip. For car, bicycle, and moped, it is denoted as POVTT, which is defined as the time taken to walk to and f:rom the parked vehicle, bicycle, or moped as well as to park and unpark. Bus and train OVTT consists of 2 parts: WSOVTT and SOVTT. WSOVTT is defined as the time spent walking to and from the bus stop or station. SOVTT is the time spent at a bus stop or station as well as in transferring from a bus to a train or vice versa.

3. OPTC represents out-of-pocket travel cost (in Dutch cents). For walking and bicycle trips, OPTC has a value of 0. For car and moped trips, it has a value equal to fuel costs in keeping with the traditional expectations of perceived motoring costs; no parking charges were included. For bus and train, OPTC equals the costs of the fares.

Socioeconomic Variables

Seven socioeconomic variables were used in the models.

1. HHINC represents annual household income. Annual income data were cod!=!d ac­cording to the following 6 classes (in guilders): (a) less than 5,000, (b) 5,001 to 25,000, (c) 10,001to15,000, (d) 15,001 to 20,000, (e) 20,001 to 25,000, and (f) more than 25,000 .

2. PER represents number of persons in the household 5 years old or older. 3. AOD represents number of private cars and noncommercial vans reported as

owned by the household divided by number of licensed drivers in the household. AOD was not permitted to have a value of more than 1.0.

4. BOP represents number of bicycles reported as owned by the household divided by number of persons 5 years old or older in the household.

5. MOA represents number of mopeds reported as owned by a household divided by number of persons 15 years old or older in the household.

6. HHPOS represents position in household. This variable equals 1 for head of household and 0 for others. Because the purpose of this variable in the modal-choice

111

model was to represent car availability, it also was assigned a value of 1 for adults with drivers' licenses who were not heads of households if there was perfect car avail­ability, that is, if AOD for that household was equal to 1.0.

7. OCC represents occupation of traveler. This was used as a simple dummy vari­able taking a value of 1 for professionals, managers, and executives and 0 for others.

A number of other variables available from the original data files, such as age and sex, were considered as was a more detailed description of the variable OCC, but these were excluded during the course of the work because of deductive considerations or simply because of the limited number of different specifications that could be estimated.

Socioeconomic variables do not vary across alternatives. Because of the form of the model, these variables somehow must be transformed either by combining them with other variables or by making them alternative-specific (that means including them in the utility function of some modes and not in others or allowing their coefficients to vary across modes).

Modal Constants

Modal constants have a totally different function than the other variables have. If the variables included in the modal utility functions fully explain modal-choice behavior, then the modal constants, or more generally, the pure alternative effects, should equal 0. Thus, with a perfect model specification and with perfect data, it can be argued that no constants are necessary. However, estimating a model without constants is not recommended in practice because the estimated values of the coefficients of the vari­ables included could be seriously affected if those variables do not explain fully the ob­served behavior. The constants therefore represent the effect of those variables that influence modal choice but are not included explicitly in the model. The formulation of the logit model is such that constants have to be alternative-specific, or, in this case, modal-specific.

If we have reason to believe that those variables that should have been included in the model to make it complete were excluded and have different values for different situations, then the values of the constants also will differ. Under such circumstances, the use of a model estimated on data for one area to predict behavior in another area, at a different time, or for a different socioeconomic group may be questionable. In a modal-choice model, the modal constants partially represent travelers' evaluations of level-of-service variables, such as reliability, comfort, privacy, and convenience, which are either difficult or impossible to measure, and unobserved preferences of travelers. An attempt was made in this study to account for the pure alternative ef­fects through the introduction of various modal-specific socioeconomic and vehicle­availability variables that usually could be expected to be highly correlated with the un­observed variables. The exclusion of constants then was considered acceptable if the coefficients of the various level-of-service variables were not affected significantly.

In a model with a maximum of 6 alternatives, only 5 (alternative-specific) constants, or coefficients of a given socioeconomic variable, can be identified. The walking mode therefore was used as the base alternative and the coefficients of modal-specific vari­ables, such as income, should be interpreted relative to the walking mode. The con­stants and the coefficients of socioeconomic variables introduced for the public transit modes were combined for bus and train primarily because of the small number of trips by both of these modes.

ALTERNATIVE SPECIFICATIONS

The initial estimation runs were deliberately restricted to rather simple specifications and were initially done with only half of the total sample (SBBl) because level-of-service data for the full SBB sample were not available until later in the study.

The results of these initial runs indicated that OPTC (whether or not it was divided

112

Table 1. Chosen modes.

Table 2. Summary of variable codes.

Table 3. ·coefficients and standard errors of in-vehicle travel time estimated for SBB 1 sample.

Work Trips in Son and Weekday Tripe Breugel and Best Sample in West of the

Netherlands Mode Percent Observations (percent)

Car Bicycle Moped Bus (and

streetcar) Train Walk Other

Code

BFCON BFHHINC BPHlllNC/PER BFMOA

BFOCC BFOVTT CAOD

CHHINC cocc COVTT FBOP

FCON FHHINC FHHINC/PER . FOCC FOVTT HHINC HHINC/PER

IVTT OPTC OVTT POVTT PT CON PTHHINC PTHlllNC/PER PTOCC SOVTT TWOCC WOVTT WSOVTT

40 28 20

5 3 4 -

156 108

79

21 11 15 -

Description

Constant Household income

23 30 11

8 2

22 4

Houru!hold 1ncanu1 divided by number of persons Mo1)~ owno.r:tiMp (number of mopeds divided by

number of persons 15 years old or older) Occupation Total out-of-vehicle travel time Car availability (number of cars divided by number

of licensed drivers) Household income Occupation Total.siut-of-vehicle travel time Bicycle ownership (number of bicycles divided by

number of persons 5 years old or older) Constant Household income Household income divided by number or persons Occupation Total out-of-vehicle travel time Household income Household income divided by number of persons in

household Jn-vehicle travel time Out-al-pocket travel costs Total out-of-vehicle travel time Parking out-of-vehicle travel time Constant Household income Household income divided by number of persons Occupation Waiting and transfer time Occupation Walking time Walking time to and from bus stop or station

standard Mode Coefficient Error Mode Coefficient

Car -0.0997 0.0584 Bus -0.759 Bicycle -0.0995 0.0258 Train -0.0881 Moped -0.1273 0.0516

Alternative to Which Applicable

Moped Moped Moped

Moped Moped Moped

Car Car Car Car

Bicycle Bicycle Bicycle Bicycle Bicycle Bicycle

All except walking Car, moped, hue, and train

Car, bicycle, and moped Bus and train Bus and train Bus and train Bus and train Bus and train Bicycle and moped Walking Bus and tram

standard Error

0.0297 0.0580

by income) had a small positive coefficient, which was not significantly different from 0. This means that OPTC does not significantly influence modal choice, at least in this case. This result corresponds with a deductive assumption made in a modal-choice study with data from Amsterdam and Rotterdam (8) in which OPTC was assumed to have no influence on the choice of whether to drive a car to work in existing Dutch urban transportation conditions. The results obtained from this study could, however, be explained by the small differences between the costs of the different modes because of the generally low level of transport costs and the relatively short length of the trips in the sample.

Previous modal-choice models have tended to introduce level-of-service character­istics as generic variables (1, 6, 10). In this study, this practice was not necessarily justified for the various components of OVTT. This is one of the few studies ever con­ducted with totally disaggregate data (data in which the home and work addresses could be located precisely), and thus the walking time to and from bus stops or stations could be appraised accurately. Parking time, however, could only be estimated because no information was available on the location of the parking place; waiting and transfer times also could only be estimated. Thus the different components of OVTT were es-

113

timated with varying degrees of reliability; aggregation to give total OVTT therefore was avoided in most of the specifications tried. The work by Stopher, Spear, and Sucher (14) on the measurement of inconvenience in urban travel suggests, however, that a division of OVTT into its various components would be preferable to aggregation into a single variable.

An exploratory run on the SBBl sample in which IVTT was used as a modal-specific variable indicated that IVTT reasonably could be applied as a generic variable because little difference was found between the modal-specific coefficients as shown by the data given in Table 3.

From the results of some of the early models estimated, HHPOS and OCC were ob­served to have no significant influence on modal choice for the sample of data used for this study.

In general, the variables were introduced into the modal utility functions in a linear form. Only in a few cases was an attempt made to explore nonlinear finite functions of the variables; this was done with the time variables and AOD, which was only used as a car-specific variable CAOD. For the time variables, a natural log transformation was tried. For the CAOD variable, 2 finite .functions were tried; one was a product of CAOD and HHINC, and the other was the product of CAOD and the natural log of IVTT by car.

The estimation results for the alternative specifications tried with the full SBB sample (390 trips) are given in Table 4; models 5 to 14 are based on the same specifi­cation for the level-of-service variables. The differences among models 5 to 14 are in the specifications of the various alternative-specific constants and the socioeconomic and vehicle availability variables. Table 5 gives for the model data in Table 4 the en likelihood function of e = 0 (which corresponds to all alternatives being equally likely), L *(O), and the en likelihood function of e = e, L *(~)* where ~~is the vector of estimated coefficients. Table 5 also gives the statistic - 2 [L (O) - L*(a)J, which is asymptotically distributed as x2 with degrees of freedom equal to the number of coefficients . p2 is a

measure of goodness of fit; it is equal to 1 - L**(o ) , or the ratio of the explained en L (~ ) ,

likelihood to the total en likelihood, and it lies b~hveen 0 and 1. p2 is p2 adjusted for degrees of freedom.

DISCUSSION OF ESTIMATED COEFFICIENTS

Values of Estimated Coefficients

The strongest deductive knowledge that we have about the estimated values of the coef­ficients is on their signs. We expect that, with everything else held equal, a deterio­ration in the level of service offered by any mode will reduce the probability of that mode's being chosen. Thus an essential requirement is that the utility of any one mode should decrease as the value of most level-of-service variables increases. (This is not the case, of course, with a level-of-service variable such as comfort if comfort was measured on a scale that increased with increasing comfort.) If a given level-of­service variable enters a utility function only once, then, with the exception of some specific transformations, the coefficient of that variable can be expected to be negative. If, however, the variable is entered in more than 1 form, such as a simple variable and in a logarithmic t r ansformation, then it is possible t hat only 1 of the coefficients need be negative. Thus in model 3 (Table 4), for instance, the s um of a (-0.14 OVTT + 0.52 enOVTT) decreases with increasing values of OVTT, if OVTT is greater than 3.5 min (OVTT was always greater than 3.5 in the data set used fo1· estimation); in fact, in this particular case, the coefficient of enOVTT was not significantly different from 0. This general requirement is satisfied in all the models estimated except for OPTC in every model in which it was included. Because the coefficient of OPTC was never found to be significantly different from O, OPTC was assumed not to have any significant influence on modal choice in this particular sample; therefore, OPTC was ultimately excluded.

There are also some deductive expectations with respect to the relationships between

Table 4. Estimation results of alternative specifications for SBB sample.

Variable or Constant

IVTT e.t JVTT OVTT "OVTT WOVTT POVTT COVTT FOVTT BFOVTT WSOVTT SOVTT OPTC/HH!NC CHH!NC CAOD CAODxHHlNC CAOD ' HHINC/ PER CAOn x 1111. IV'T'T co cc FCON FHH!NC FHH!NC/PER FBOP FOCC BFCON BFHHINC 13 FHHINC/P ER BFMOA BFOCC TWOCC PT CON PTHHINC PTHHINC/ PER PTO CC

IVTT b:IVTT OVTT 2, QVTT WOVTT POVTT COVTT FOVTT BFOVTT WSOVTT SOVTT OPTC/ HHINC CHHINC CAOD CAQDxHHlNC CAOD < HHlNC / PER CAOD K 1-. JVTT cocc FCON FHH!NC FHH!NC/PER FBOP FOCC BFCON BFHHINC BFHHINC/ PER BFMOA BFOCC TWOCC PT CON PTHHINC PTHHINC/ PER PTO CC

Model 1

Stan-Coeffi- dard cient

· 0.0673

- 0. 1193

0.0066

0, 5077

Error

0,0091

0 .0172

0 .0101

0.4396

0.3254 0.3514

-0.7645 0. 3517

1.66! 5 0,5976

Mode l 8"

Stan-Coe rn- dard cient Error

- 0 .0649

-0,2527 -0.2255

-0, 1113 -0.0834

0 ,0071 -0 .5764

0 ,7721

-0.1213

-0 .5332

0.8209

0.0197 0.0497

-0.4594

0.1066

0.0105

0.0535 0. 1013

0. 0220 0.0341 0.0113 0.2616 0.5034

0.4928

0 2421

0 .2409

0 .4537 0.4537

0.2696

0.5097

Model 2

Stan-Cue({i- dan.J cient

-0.0757

-0. 1676

-0.3290 -0,2501 -0, 5141 -0. 1206 -0.0674

l.1363

Model 9

Error

0,0106

0.0291

0.0003 0.1015 0.1040 0, 0210 0, 0236

0.0520

Stan-Coern - dard clent Erro r

-0,0643

-0.2511 -0.2145

- 0.1101 - 0.0820

0 0071 - 0.5099

0,7636

-0. 5393

- 0.0236

-0.4553

0.0102

0.0530 0.0907

0.0213 0.0340 0.0113 0.2559 0.5024

0.2408

0.2406

0.2690

Model 3

Stan-Coetli- dard cient

-0.0672 -0.0343 -0, 1419

0. 5106

0,0006

0,2400

Error

0.0116 0,5016 0.0346 0. 7366

0.0115

0. 1110

0 74R6 0. 6009

-0.3064 0.4712

1.6904 0, 8316

Model 10

Stan­Coem- dard cient Error

-0.0644

-0.2201 -0. 2539

-0, 1041 -0.0936

0.0210 -0 5066

1.5314

-0. 6860

1. 5790

-0. 0091

1.0492

0.0103

0.0527 0_0920

0.0214 0.0345 0.0119 0.2567 0.5444

0.2440

0,3841

0. 2530

0,7457

Model 4

l..'oetl1 cient

-1 ,5639 -0. 1610

0.0304

0.4966

Stan­dard Error

0.3971 0,0234

0, 0100

0. 1162

1.4463 0. 5795

0 ,3563 0-3673

3.1672 0.7681

Mode l 11

Stan-Coeffi- dard cient Error

-0.0665

- 0.12 57 - 0.3559

-0.0907 -0,0853

0,0109

2. 1651

1.4690

2.2659

0.0094

0.0266 0.0706

0.0193 0 0306 0.0113

0. 4753

0.3399

0. 5556

Model 5

Stan-coern- tl:inl clent

-0.0644

· 0,1661 -0 .2933

-0.1195 -0.0962

0.0081

0.2435

Error

0.0101

0.0321 o.0794

0.0218 U.Ua44 0 0107

0_1416

0.0286 0. 1136

-0.2562 0, 1081

0. 1099 0 1823

Model 12

Stan-Coeffi- dard c ient Erro r

-0.0715

· 0.1333 · 0.3590

-0_1034 -0,0511

2.2928

1.3272

-0.0132

0.0090

0.0266 0.0795

0.0193 0.0216

0.4709

0. 3263

0. 5375

Model 6

Stan-Cueffi- Uard cient

-0. 0732

-0. 1545 -0.2372

-0,1149 -0.0887

0.0119

0.2963

Error

0.0101

0.0293 0.0727

0.0209 0.0329 0 0105

0.4163

0.2400 o.3527

-1.1043 0. 3626

0, 1670 0.4505

Model 13

stan-Coerti- dard cient Error

-0.0721

- 0. 1095 - o 2675

-0. 1269 -0.0824

2.2025

1.4936

0.2201

1. 7404

0. 0092

0 0201 0 0919

0.0230 0.0209

0. 4690

0.3410

0. 5527

0.9155

Model 7

Stan-coeffi- dard cient

-0,0664

-0.2535 -0.2314

-0. 1131 -0.003 6

0.0067 -0. 5690

0 7647

Error

0.0107

0.0535 0. 1010

0.0222 0,0341 0.0113 0.2616 0. 5046

-0. 5294 0.2422

0 3037 0. 5665

-0.0109 0.2411

-0.1390 0.6262

-0 4557 0.2707

0.1654 0,6759

Mode l 14

Slan-Coe ffi- dard cient Error

-0.0600 0.0093

-0.1192 0.0295 -0. 3260 0,0946

- 0.1136 0,0234 -0.0856 0.0288

l.0056 O. IBOO

J.4340 0.3211

0.6609 o. 5536

1.5057 0.9252

•3 different 11ersions of model 8 were estimated, each of which incorporated only 1 of the 3 11ariables COCC, TWOCC. and PTOCC; atl ot lhe coefficients, except lor those of TWOCC and PTOCC, and standard errors are those for the model in which COCC wasjncluded.

Table 5. Likelihood functions and other data for models in Table 4.

Model

l 2 3 4 5 6 7 8 9

10 11 12 13 14

L•(O)

-435.13 -435.13 -435.13 -435.13 -435.13 -435.13 -435.13 -435.13 -435.13 -435. 13 -435.13 -435.13 -435.13 -435.13

L•(S)

-272.81 -271.69 -271.17 -292.60 -269.14 -272.00 -266.55 -266.03 ·266.06 -257.59 -260.69 -270.10 -266.29 -260.54

x'

324.63 326.06 327.92 285.05 331.97 326. 10 337. 16 336.59 366.53 355.07 332.60 330.04 333.60 349.17

p'

0.37 0.38 0.30 0.33 0.30 0.37 0.39 0.39 0.39 0.41 0.38 0.30 0.30 0.40

p'

OH OH OH on 0.37 OH on 0.30 on ow on OH 0.30 ow

115

certain coefficients of level-of-service attributes. For example, one would expect the coefficient for an OVTT var iable to be greater than the coefficient for IVTT. In all the specifications tried, IVTT was, indeed, found to have a lower coefficient than any of the OVTT variables; the coefficients of walk as a mode WOVTT and WSOVTT are almost equal and have approximately twice the value of the coefficient for IVTT. Thus walking appears to be twice as inconvenient as riding in or on a vehicle. This relationship cor­responds to the usual assumption used to create generalized costs in Wilson-type models in the United Kingdom, where the coeffi cient fo r excess time is us uall y taken to be twice that for IVTT (9). Wait time at a bus s top or station appears to be more inconvenient than IVTT but not so bu1·densome as walki ng. This is a departure from t he us ual as­sumption previously mentioned as well as from U.S. studies in which the coefficient for wait time usually is taken to be 2.5 times that of in-vehicle time (11). However, the relatively low coefficient of wait time in this sample might be attributable to a highly reliable transport service and therefore to an overestimate of the value of wait time. It also could reflect other errors in estimating the wait times used in this study. It also should be noted that, compared with the coefficients of other level-of-service var­iables, the coefficient for SOVTT has a relatively large variance. This probably is due to the low variability of headways in the public t ransit services available to the indi­viduals in the sample (that is, low variability in SOVTT values).

Expectations with respect to the values of both the constants and the coefficients of the socioeconomic variables are more complicated and rely on very limited or non­existent past experience. One particular problem encountered in the design of the study was the limited availability of results from previous studies using similar models es­pecially for European circumstances.

If everything is equal, one would expect that as car ownership increases the proba­bility of choosing car as the mode of transport would increase and thus that the proba­bility of choosing other modes would decrease. One would therefore expect that the coefficient for CAOD would be positive and, for similar reasons, that the coefficients of both bicycle and moped availability also would be positive.

Household income and modal constants appear in the utility function of more than 1 mode , and, therefore, interpretation must r ela te to their r elative values and not their absolute values. In model 5 (Table 4), for example, the relative values of the coeffi­cients of household income indicate that, as household income increases and everything else is held constant, the increase in the probability of using car is relatively greater than that of using other modes, and the probability of choosing a moped will decrease relative to all other modes . Between these extremes are (a) public transit, which cle­c1·eases in relation to car but increases in relation to the other modes; (b) bicycle, which decreases relative to car and public transit a nd increases r elative to walking and moped; and (c) walking, which is a base mode. Thus the probability of walki ng in­creases relative to moped but decreases relative to all other modes; this could reflect the socioeconomic status of a moped as a transit mode.

The modal constants and socioeconomic variables could be interpreted as represent­ing the pure preferences for the alternative modes if the utility derived from the level­of-service characteristics was equal across all modes. A direct interpretation of this kind i s easier when all the level-of-s ervice cha ract er istics are i ntroduced as generic variables . For example these variables in model 1 (Table 4) imply that, if IVTT and OVTT are equal across modes, t hen an individual with perfect car availability (AOD = 1) will rank the modes in the following order: public transit, car, bicycle, walking, and moped. The place of public transit in this pure ranking appears to be too high. However, the pure ranking for a person with all modes perfectly available, which is given by model 13 (Table 4) (which represents an improved specification), is: car, public tran­sit, bicycle, moped, and walking. This preference ordering agrees more closely with deductive expectations; this ranking also is implied by model 14 (Table 4), which was the last specification estimated with this sample and which we considered to have the most satisfactory specification of the models estimated.

116

Stability and Statistical Reliability of Estimated Coefficients

The reliability and stability of the estimated coefficients can be observed in several ways including the relative magnitudes of the standard errors and the variability of the estimates across both different specifications and different subsamples.

The magnitude of the standard errors of the estimated coefficients is relatively small (compared with the magnitude of the estimated coefficients) for the travel-time variables but is relatively higher for some modal constants and socioeconomic variables, particularly the moped-specific variables (Table 4). This also could be observed from the variability of the estimated coefficients of the same variables across different spec­ifications.

From Table 4, the coefficients of the travel-time variables are quite stable, in par­ticular the coefficient of IVTT. On the other hand, some of the coefficients of the socio­economic variables and the constants appear to be less stable. This pattern also was observed in the comparison of different subsamples.

As recorded in the section on data, 2 types of subsamples were created from the SBB sample. One was a random division into SBBl and SBB2, a division that proved of value in the evaluation of the statistical stability of the estimated coefficients compared with the estimated values of the standard errors. The second was a division into 2 selected geographic subsamples, SB and B. This allowed a comparison of coefficients between 2 different areas; differences between coefficients from the 2 areas were used to trace possible specification errors. We assumed that travel behavior in both areas is similar and, therefore, that a specification that has similar coefficients for both areas is supe­rior to a specification with divergent estimates.

Table 6 gives the estimation results for models 5, 13, and 14 for the different sub­samples. From this table, one can see that the coefficients estimated for model 14 are quite stable between the SBB and B samples. The variability between the estimates of the coefficients for SBBl and SBB2 is considerably higher, but this can probably be at­tributed to the fact that the standard errors are larger because of smaller sample sizes. This pattern of decreasing standard errors with increasing sample size for the 3 models and the subsamples as shown by the data given in Table 6 is shown in Figures 1, 2, and 3. These figures indicate that an increase in sample size beyond 300 observations does not reduce significantly the standard errors of the coefficients of most of the var­iables. This pattern suggests that, for these models, a desirable sample size would be between 300 and 400 observations.

To compare the stability of the estimated coefficients between 2 independent random samples, one would need at least 600 observations rather than the 400 observations available. Samples larger than 300 to 400 observations, however, might be necessary if more or other socioeconomic variables were to be included. With the existing sample, these have been found to have very large standard errors in contrast to coefficients of level-of-service variables for which reasonable levels of reliability at smaller sample sizes were achieved.

Geographical comparison of the estimated coefficients between B and SB is not conclusive because of the small number of observations in the SB sample. However, the stability between SBB and B seems satisfactory in view of the fact that, although B is included in SBB, there are still significant differences between both the means and distributions of several of the explanatory variables.

Table 7 gives likelihood functions and other data for the information in Table 6.

ANALYSIS OF ALTERNATIVE SPECIFICATIONS

The specification for model 14 appears to be the most satisfactory of all those tried. The reasoning leading up to this conclusion, as well as aspects of some of the other models estimated, is discussed in this section.

As discussed in the section on alternative specifications, the formulation of the level­of-service variables in models 5 to 14 seems to be superior to that used in models 1 to 4. The coefficients of all the level-of-service variables in models 5 to 14 have the ex-

Table6. Estimation results for data sets for models 5, 13, and 14.

SBB SBBl SBB2

Variable or standard standard Model Constant Coefficient Error Coefficient Error

PTHHINC 0.1099 0.1823 0.3866 0.3205 FHHINC 0.0286 0.1138 0.3703 0.1777 BFHHINC -0.2562 0.1081 0.0265 0.1711 CAOD,HHINC 0.2435 0.1418 0.5316 0.2341 lVTT -0.0644 0.0101 -0.0739 0.0155 WOVTT -0.1661 0.0321 -0.1365 0.0526 POV TT -0.2933 0.0794 -0.2356 0.1225 WSOVTT -0.1195 0.0218 -0.0887 0.0306 SOVTT -0.0962 0.0344 -0.1803 0.0650 OPTC/HHINC 0.0081 0.0107 0.0278 0.0175

13 IVTT -0.0721 0.0092 -0.0636 0.0146 WOVTT -0.1095 0.0281 -0.1074 0.0494 POVTT -0.2675 0.0919 -0.3036 0.1459 WSOVTT -0.1269 0.0238 -0.0649 0.0331 SOVTT -0.0624 0.0269 -0.1121 0.0516 CAOD 2.2025 0.4690 3.4796 0.6296 FBOP 1.4936 0.3410 2.3249 0.5569 BFMOA 0.2261 0.5527 1.3823 0.8503 PT CON 1.7404 0.9155 1.2698 1.5645

14 IVTT -0.0600 0.0093 -0.0679 0.0148 WOVTT -0.1192 0.0295 -0.1210 0.0532 POVTT -0.3260 0.0946 -0.3753 0.1580 WSOVTT -0.1136 0.0234 -0.0701 0.0317 SOVTT -0.0856 0.0288 -0.1167 0.0511 CAODx 01lIVTT 1.0056 0.1800 1.5746 0.3570 FBOP 1.4348 0.3211 2.2351 0.5483 BFMOA 0.6689 0.5536 1.8694 0.8818 PT CON 1.5057 0.9252 1.0927 1.5822

Figure 1. Standard error of estimated coefficients and sample size for model 5. ~

.l! 210% c 200)ll

Figure 2. Standard error of estimated coefficients and sample size for model 13.

f 100%

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-0.0633 -0.2722 -0.4835 0.0739

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1.5391 0.9527

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-N

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100 200 300

No of observations

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100 200 300 No, of observo1ions

standard Error

0.2362 0.1678 0.1576 0.1945 0.0140 0.0447 0.1140 0.0333 0.0361 0.0137

0.0123 0.0349 0.1247 0.0376 0.0339 0.6052 0.4516 0. 7479 1.1724

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B

Coefficient

-0.0955 -0.2247 -0.4710 -0.0685 -0.0689 -0.2075 -0.3418 -0.1333 -0.0704 -0.0071

-0.0769 -0.1098 -0.2732 -0.1374 -0.0766

1.4234 1.3537 0.1806 1.7068

-0.0688 -0.1164 -0.3241 -0.1269 -0.0028 0. 7254 1.3529 0.5000 1.5553

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SB -Standard Standard Error Coefficient Error

0.2274 -0.0528 0.1626 0.2630 0.1563 -0.0351 0.1860 0.6278 0.0117 -0.0501 0.0426 -0.2046 0.0969 -0.2382 0.0272 -0.1102 0.0380 -0.1047 0.0144 0.0335

0.0110 0.0313 0.1106 0.0264 0.0307 0.5504 0.3969 0.6329 0.9961

0.0122 -0.0338 0.0324 -0.2381 0.1130 -0.3785 0.0280 -0.0881 0.0308 -0.0594 0.2145 1.6427 0.3724 1.4551 0.6267 1.3234 1.0075 0.4079

~ i.i-

100 200 300

No. of observations

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0.6001 0.1980 0.1775 0.2766 0.0265 0.1322 0.1597 0.0519 0.1200 0.0268

0.0208 0.1621 0.1939 0.0549 0.0856 0.4336 0.6911 1.4021 2.6117

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No_ of observations

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Table 7. Likelihood functions and Number or other data for models in Table 6. Model Data Set Observations L'(O) L'(B) x' p' p'

SBB 390 -432.13 -269. 14 331.97' 0.38 0.37 SBBI 182 -201.98 -109.53 184.89' 0. 46 0. 44 $882 208 -233.15 - 149.72 166.86' 0.36 0.34 B 241 -282.25 -186.92 190.65' 0.34 0.33 SB 149 -152.88 -73,09 159.57' 0. 52 0. 50

13 SBB 390 -435.13 -268.29 333 , 68b 0.38 0.38 SBBI 182 -201.98 -106.2 6 191.4-5b 0.47 0.46 $882 208 -233. 15 - 153. 41 159.47b 0.34 0.33 B 241 -282.25 -188.96 1B6.58b 0.33 0.32

14 SBB 390 -435.13 -260.54 349.17° 0 . 40 0.40 SBBl 182 -201 ,98 -101 .43 201.11° 0. 50 0. 49 SBB2 208 -233.15 -149.92 166.44° 0. 36 0.34 B 241 -282. 25 -186.02 192.47° 0.34 0.33 SB 149 -152.87 - 68.29 169 .18° 0.5 5 0. 54

"Degrees of freedom = 10. bDegrees of freedom = 9 coegrees of freedom= 9.

Table 8. Disaggregate prediction results.

Pe rcentage or Shares Sample Type of

Sample Size Data Walking Car Bicycle Moped Bus Train

SBB 390 Predicted 2.75 40.01 27.60 21.43 5.66 2.54 Observed 3,85 40.00 27 .69 20.26 5.38 2.82

SBBI 182 Predicted 2.88 40.50 29. 13 19.10 5.55 2.85 Observed 2.75 42.86 29 .67 18. 13 3.30 3.30

SBB2 208 P redicted 2.65 39.57 26. 27 23.48 5.76 2.27 Observed 4.81 37. 50 25.96 22.12 7.21 2 .40

B 241 Predicted 3.03 31.93 31.29 22 .89 6.43 4 .11 Observed 5.39 29.46 31.12 22.82 6.64 4.56

SB 149 Predicted 1.95 53. 07 21. 64 18.92 4.42 Observed 1.34 57.05 22.15 16.11 3.36

Zones 100, 103, and 110 to 37 Predicted 0 44.92 6.96 14.09 15.03 18.99 Eindhoven center Observed 0 48.65 2 .70 13.51 16. 22 18,92

Zones 100, 103, and 110 to 74 Predicted 0 45.26 15. 50 24.92 ID. BO 3.52 Eindhoven e lsewhere Observed 0 37.64 17.57 28.38 10.81 5,41

Zones 200 and 210 to 19 Predicted 0 61.30 12.35 14.25 12.11 0 Eindhoven center Observed 0 68.48 5.26 15.79 10.53 0

Zones 200 and 210 to 52 Predicted 0 59.47 14.81 19.26 6.45 0 Eindhoven elsehwere Observed 0 63.46 19,23 13. 41 3.65 0

Zone 100 total 86 Predicted 2. 61 53.78 22.1 6 15.17 6. 28 0 Observed 2.33 59.30 22.09 11.63 4.65 0

Zone 210 total 23 Predicted 1. 61 49.43 26.15 21.72 1.09 0 Observed 0 56.52 17 .39 26.09 0 0

Table 9. Aggregate prediction Percentage ol Shares results. Sample Type or

Sample Size Data Car Bicycle Moped Bue Train

Best to Eindhoven, 46 Predicted 66. 85 8.43 20.37 2. 78 1.59 zone 2 Observed 41.30 26.09 30.43 0 2.17

Best to Elndhoven, 40 Predicted 60.35 4.48 17.83 6.98 8.45 zone 3 Observed 45.00• 2.50 15.00 17.50 20.00

Son and Breugel to 27 Predicted 64.03 8.95 25.22 1.78 Eindhoven, zone 2 Obse rved 62. 16 18.92 13 . 51 5.41

Son and Breugel to 25 Predicted 70.96 6.72 20.16 2 . 16 0 Eindhoven, zone 3 Observed 64.00 8.00 20.00 8.00 0

119

pected signs (except for OPTC, which is not significant) as well as the expected relative values. Therefore, any preference among specifications 5 to 14 must be based on the behavior of the socioeconomic variables and the model constants.

Models 5 and 6 have identical specifications except for household income, which was included in model 5 but replaced in model 6 by income per person. It would seem rea­sonable that the pure modal preferences would be more closely related to the total household income rather than the average income per person after income pooling. Al­though model 5 has a slightly better goodness of fit than model 6 has, the estimation results are by no means conclusive evidence that model 5 is, indeed, any better than model 6. However, this, together with the previous statement, caused us to consider model 5 superior to model 6.

In models 7, 8, and 9, the car-specific variable CAOD x HHINC was split into 2 separate variables CAOD and CHHINC. In addition, an attempt was made in models 7 and 8 to introduce OCC as a variable (in the form of a modal-specific variable), but in neither model were any of its coefficients significantly different from 0. Model 9 was considered to be less satisfactory than model 5 because of the relatively larger variance of the coefficient of CAOD; this is probably attributable to a high level of collinearity between car availability and household income.

The specification of model 10 includes the same variables as model 9 with the ad­ditional variables bicycle BFOP and moped availability BFMOA. In model 10, however, the variances of the coefficients of the socioeconomic variables were large, and thus it appeared desirable to select only a subset of these variables for the following models. This was done in models 11, 12, and 13 in which only the vehicle-availability variables were included. These variables were selected because it seemed reasonable to assume that they have a greater direct bearing on modal choice than household income has. Furthermore, the coefficients of these variables in earlier models were more signifi­cant than those of the income variables.

Models 11 and 12 are identical except for OPTC, which was excluded from model 12. In model 13, a public transit constant PTCON was reintroduced. Because it is highly probable that the specification of model 12 was not perfect, and that, therefore, the absence of a public transit constant could considerably affect the values of the coef­ficients of other variables, model 13 was considered the best of the series of models 7 to 13.

Thus far, therefore, model:;; 1 to 13 have been evaluated and models 5 and 13 have been selected as 2 of the best models. These 2 models represent 2 essentially alterna­tive specifications of the socioeconomic variables. Model 5 is based on modal-specific income variables, and model 13 is based on modal-specific vehicle-availability variables. These 2 models also were estimated for the various subsamples and the results of these estimations are given in Table 6. A comparison of these 2 sections of Table 6 and a comparison of Figures 1 and 2 show that it is evident that model 13 is more stable than model 5. From a consideration of both goodness of fit and the significance of the coefficients, one can conclude that model 13 is superior to model 5.

Examination of the variability of the estimated coefficients for the different sub­samples of model 13 in Table 6, however, shows the coefficient of CAOD to be p~rticu­larly unsatisfactory. Examination of the characteristics of the various subsamples showed that the coefficient of CAOD had a smaller value in those subsamples having a shorter average trip length and that it had a larger value in subsamples with a longer average trip length. It therefore seems reasonable to assume that, when a car is perfectly available to an individual, the longer the trip the more likely he or she is to choose the car. When a car is not perfectly available, and there is some degree of competition among different users of a car within a household, it would seem reason­able to expect that those individuals making longer trips will tend to have priority in use of the car over those making shorter trips. Thus it seems reasonable to specify the coefficient of car availability as a function of trip length. If this is so, then it could be expected that this function will show a diminishing marginal effect with in­creasing trip length and therefore the CAOD variable was multiplied by the natural log of IVTT by car. This change was implemented in model 14.

A comparison of model 13 with model 14 (Table 6 and Figures 2 and 3) shows that

120

model 14 is superior to model 13 in terms of stability of the coefficients, significance of the coefficients, and goodness of fit. Thus, model 14 appears to have the most satisfactory specification of those models estimated and given in Table 4.

PREDICTION TES TS

'l\vo types of prediction tests were applied. The first was a disaggregate test designed primarily to determine how well the model fit the observed data. The second test was with aggregate data and was designed to test the applicability of the model for aggregate predictions.

Disaggregate Predictions

In disaggregate predictions, explanatory variables are used to predict individual modal­choice probabilities. These individual probabilities are summed across a group of travelers and compared with the observed modal shares for the same set of individuals. When the group of travelers consists of the complete set of individuals used in the es­timation of the model, this test can be viewed as a test of goodness of fit. However, the estimation procedure used in this study guarantees that, if a model specification includes a constant, the modal shares calculated in such a test will be perfect for the alternative to which that constant relates. For model 14, this implies that a disaggre­gate prediction test with the complete data set used in model estimation will reproduce perfectly the total public transit share because PTCON was included. However, be­cause no constant was used for any of the remaining 4 modes, this test is still meaning­ful for the split between the 2 public transit modes and the 4 other modes. The results of this test are given in the first row of Table 8, and as has been stated, one can see that the split between public transit and the other 4 modes is reproduced perfectly. The results among the individual modes within these two sets, however, also are extremely satisfactory.

To provide a thorough test of the model, one would ideally apply it to a second set of data not used in the model estimation. Unfortunately, because of budget and time con­straints pertaining to this study, a second set of data was not available. Instead, the test was applied to several subsets of the data set used for model estimation; the re­sults of these also are given in Table 8. The subsets used include the subsamples SBBl, SBB2, SB, and Band 2 other types of subsamples that were created. The first of these consisted of groups of individuals with a home address in a specific zone and the second was formed of groups of individuals with a home address in a specific zone and a work address either in the center of Eindhoven or elsewhere in Eindhoven.

All the modal shares of these various subsets were predicted satisfactorily. The differences between the observed shares and the predicted shares are minimal for the larger subsets (more than 100 observations). For the smaller subsets, the relative differences between the observed and predicted shares are especially large for bicycle and moped. There is, however, a tendency for some mutual compensation here in that, when one share is overestimated, the other is usually underestimated. This means that the total share of bicycle and moped is more satisfactorily reproduced than the individ­ual shares are.

Aggregate Predictions

In normal predictive work, disaggregate data are not usually available, and thus the model must be applied by using aggregate data. Simple substitution of group averages for the explanatory variables will result in a biased forecast of the average probability or share; this bias will disappear only if all individuals in the group for which predic­tions are being prepared are identical in terms of the values of all the explanatory var­iables. Between the 2 extremes of disaggregate predictions and use of averages for the

121

entire group in aggregate predictions, identifying a stratification scheme or system of market segmentation so that the aggregation bias can be assumed to be small and, within the context of the application, negligible is possible.

Table 9 gives the results of aggregate predictions prepared with model 14 for 4 0-D pairs by using a very coarse zoning system. For this application of the model, all the travelers making a trip between any pair of zones were grouped together, and the av­erage value of each variable for the members of that group was used. Furthermore, no account was taken of different sets of available modes for individuals in the group. The calculated shares are clearly not satisfactory in comparison with the observed shares. In particular, the share of car trips is significantly overestimated for the first 2 groups, which consist of people residing in Best. Although the car-share fore­casts for the Son and Breugel groups are better, they are not satisfactory. The di­vergence between the observed and predicted shares serves as a good illustration of the errors that can occur from simply taking averages for each individual variable and directly applying them in the model.

In Son and Breugel, the majority of the residents are car owners; in Best, many families are without cars. Therefore, the model evidently performed better when there were high levels of car ownership than when there were lower levels of car ownership. Through the use of one set of average values of all variables, including CAOD, applied to all travelers, cars have effectively been made available to people for whom they were not available.

The forecasting error can be reduced by a stratification of the travelers between any pair of zones. Of course, the ultimate stratification is that of complete disaggre­gation, but this would also produce some prediction errors, the magnitude of which would depend on the validity of the model itself. The errors in the predictions given in Table 9 are therefore a combination of both disaggregate prediction errors and an ag­gregation bias. Given a specific model, reducing the aggregate prediction error by attempting to reduce the aggregation bias is possible.

In Table 10, the results of aggregate predictions are given for travelers between the same sets of specific zone pairs as were used for the work summarized in Table 9, but now it is stratified into those who are car owners and those who are not car owners. This sort of stratification is quite common in travel demand forecasting (15), and it is evident from the analysis of the differences in the errors of the predicted shares of car between Son and Breugel and Best that such a stratification scheme would improve the aggregate predictions. The improvement in the aggregate predictions that is due to stratification by car availability is shown by the data given in Table 11. Further strat­ification by choice set (such as by moped availability) could be expected to lead to im­proved aggregate predictions. The results given in Tables 10 and 11 can be considered acceptable in view of the coarse zoning system adopted and the consequential effects of this on the values of the level-of-service variables applied. Furthermore, for each in­dividual group, there is also an error in the observed share, relative to the total popu­lation, that is due to sampling. Because this error increases with decreasing sample size, the greater the number of the observed travelers is that is used to compute the observed aggregate share, the more meaningful the aggregate prediction tests are. Thus an adequate evaluation of the aggregate prediction errors can be undertaken only for those zone pairs with a high trip density, that is, those where the error in the ob­served share could be assumed to be negligible.

The disaggregate prediction tests have demonstrated that model 14 reproduces the average choice of individuals satisfactorily. The aggregate predictions have much more important implications with respect to the usefulness of the models because the model is tested in the same way as the way in which it will be applied generally. The aggregate modal-choice predictions based on a stratification of travelers into those with a car available and those without a car available can be considered satisfactory given the limitations of the data used for this test. This implies that the model can be applied usefully to aggregate predictions in transportation planning studies.

122

Table 10. Aggregate prediction results with market stratification by car availability.

Per centage of Shares Car Sample Type of Available Sample Size Data Car Bicycle Moped Bus Train

Yes Best to Eindhoven, 30 Predicted 81. 67 4.47 11.10 1. 73 1.03 zone 2 Observed 63.33 13.33 23.33 0 0

Best to Eindhoven, 29 Predicted 70.93 3.07 15. 59 5. B3 4.59 zone 3 Observed 62.07 3.45 6.90 17.24 10.34

Son and Breugel to 30 Predicted 74.10 6.00 18. 50 1.07 Eindhoven, zone 2 Observed 76.67 20.00 3.33 0

Son and Bruegel t o 21 Predicted 77.24 4.71 16. 71 1.29 Eindhoven, zone 3 Observed 76. 19 4 .76 14.29 4. 76

No Best to Eindhoven, 16 Predicted 0 22.69 68.81 5.56 2. 88 zone 2 Obser ved 0 50.00 43. 75 0 6.25

Best to Ei ndhoven, 11 Predict ed 0 12.00 35.36 21.09 31.54 zone 3 Observed 0 0 36.36 18.18 45. 45

Table 11. Aggregate prediction results with and without market stratification.

Percentage of Shares Sample

Sample Size Type or Data Car Bicycle Moped Bus Train

Best to Eindhoven, 46 P r ediction without stratification 66.85 8. 43 20.37 2.7 8 1. 59 zone 2 Prediction with stratHi cation 53 .26 10.81 31.17 3.06 1.67

Observed 41. 30 26.09 30.43 0 2.17

Best to Eindhoven, 40 Prediction wit hout s trat iri cation 60. 35 4.4 8 17.83 8.98 8.45 zone 3 P red iction with st r atification 51.42 5. 53 21.03 10.03 12.00

Observed 45,00 2.50 15.00 17.50 20.00

CONCLUSIONS

The modal-choice model for work trips described in this paper was probably the first attempt to consider the full variety of travel modes available in medium- and small­sized Dutch communities where the conventional binary choice model for car and public transit that commonly is used is clearly not suitable. Although the models developed require further work before they could be considered standard operational production techniques, existing models could serve usefully in various transportation planning s tudies .

A number of conclusions can be drawn from the models estimated. One is that the probability that anyone will choose a given mode is determined largely by factors other than the level of service offered by that mode. If a car is perfectly available to a traveler, then there is a very high probability that he or she will choose it regardless of the characteristics of the alternative modes. The policy implications of this as proposals for traffic restraint in urban areas increase, at least in Europe, are con­siderable. The estimation results tend to confirm the general assumptions about the relative weights of IVTT and OVTT, although it would appear that there could be sig­nificant differences in the evaluation of different types of out-of-vehicle travel time. IVTT would, on the contrary, seem to be viewed similarly for all modes. Travel costs do not significantly influence modal choice for the particular data set, nor do socio­economic characteristics other than vehicle availability.

It has been suggested previously that the estimation of disaggregate models requires fewer observations than does the calibration of aggregate models. Estimating the same model with different data sets tends to confirm this belief in that the marginal value of increasing the sample size above some 300 observations was found to be small.

The transformation of disaggregate models to aggregate models for use as predictive models presents a number of theoretical problems. It would seem possible, however, that, for all practical purposes, the effects of the problems can be minimized by use of market stratification.

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ACKNOWLEDGMENTS

This paper is based on the results of a study carried out by Buro Goudappel en Coffeng b.v., and Cambridge Systematics, Inc., under contract to Projectbureau Integrale Verkeers- en Vervoerstudies, Ministerie van Verkeer en waterstaat, Netherlands. The permission of the Projectbureau to utilize the results of that study is gratefully acknowledged. However, the opinions expressed are ours and not necessarily those of the Projectbureau. We wish to acknowledge the advice and encouragement of the 2 project monitors, Chresten J. Steilberg and Klaus Broersma, of the Projectbureau. The assistance of Koos Mars, Jan Jetten, and Meindert Bovens in the execution of the study also is acknowledged.

The material in this paper is drawn from a report that is available elsewhere (_!).

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